Memory foam has advantages over regular foam. Memory foam is temperature and weight sensitive, meaning it will mould to the contours of one's feet. When you put on the slippers, you will feel your feet "melting" into the foam as the temperature of your feet cause the foam to become more pliable.
If you have naturally cold feet, these slippers will likely keep your feet warmer than normal slippers. This is because memory foam tends to absorb body heat and not release it quickly, resulting in a toasty warm temperature. However, if your feet are naturally hot, you may want to avoid the Tempurpedic slippers.
With regular use, the memory foam will eventually lose its "memory," meaning that it will no longer effectively mould to the contours of your feet. However, you should expect to get at least a couple of good years from the slippers. In addition, while memory foam can sometimes off gas, that is, give off a chemical-like smell when new, Tempur material typically does not have a substantial off gas problem.